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Theorem ls-unique-strng

⊦ (o[ls(r, x)] * R)[rs, cf, af] ∧ (o[ls(r, x0)] * R0)[rs, cf, af] → (x ≠ x0 ↔ false)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: ls-push,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 6
Used lemmas: ls-rec, ls-null, ls-base,
Used spec theorems:
- Used simplifier rules:
  - list/c-06
  - cell/inj
  - embed-aux/cell-heap-aux/map2
  - list/e-01
  - maplet/cell-heap-aux/map-null
  - heap-fun/cell-heap-aux-heap-aux/ex1-shift
  - heap-sep/cell-heap-aux/sep-com
  - heap-sep/cell-heap-aux/sep-ass
  - embed-aux/cell-heap-aux/embed-split
  - embed-aux/cell-heap-aux/lift-ex-r
  - list/a
  - list/c
  - embed-aux/cell-heap-aux/embed-and
  - embed-aux/cell-heap-aux/lift-emp
  - embed-aux/cell-heap-aux/lift-prop
  - heap-sep/cell-heap-aux-heap-aux/and-ass
  - heap-sep/cell-heap-aux-heap-aux/and-com
  - heap-sep/cell-heap-aux/and-ass
  - heap-sep/cell-heap-aux/and-com
  - heap-sep/cell-heap-aux-heap-aux/prop-shift
  - heap-sep/cell-heap-aux-heap-aux/emp-sep
  - heap-sep/cell-heap-aux-heap-aux/sep-ass
  - heap-sep/cell-heap-aux-heap-aux/sep-com
  - embed-aux/cell-heap-aux/and-split
  - heap-fun/cell-heap-aux-heap-aux/prop
  - heap-sep/cell-heap-aux/false-rev
  - heap-sep/cell-heap-aux/false-and
  - embed-aux/cell-heap-aux/lift-false
  - heap-sep/cell-heap-aux-heap-aux/false-sep
  - heap-fun/cell-heap-aux-heap-aux/prop-false